To solve the problem, we first analyze the information presented:
- It mentions the angle measure \( \angle K \) along with \( (5y - 19)^\circ \) and \( 56^\circ \).
- Typically, in a triangle, the sum of the angles must equal \( 180^\circ \).
Part 1:
We are tasked with writing an equation to find the value of \( y \). Considering the angle measures given and understanding that they are part of a triangle, we can use the equations provided.
To find \( y \), we can set up the equation as provided:
\[ 5y - 19 = 56 \]
Part 2:
To find \( \angle K \), we only need the expression for \( \angle K \) if we substitute the value of \( y \).
Starting with the equation we wrote:
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From the equation: \[ 5y - 19 = 56 \]
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Solve for \( y \): \[ 5y = 56 + 19 \] \[ 5y = 75 \] \[ y = 15 \]
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Finding \( \angle K \): Now we substitute \( y \) back into \( \angle K \): \[ \angle K = 5y - 19 \] Substituting \( y = 15 \): \[ \angle K = 5(15) - 19 = 75 - 19 = 56^\circ \]
Thus:
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The answer to Part 1 is: \[ 5y - 19 = 56 \]
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The answer to Part 2 is: \(\angle K = 56^\circ\)